Let y=3^(x). Find (d^(2)y)/(dx^(2)) (d^(2)y)/(dx^(2))=

Find Second Derivative: Now, we need to find the second derivative (d^(2)y)/(dx^(2)). We differentiate dy/dx = 3^(x) * ln(3) with respect to x again. Using the product rule, (d/dx)(u*v) = u'v + uv', where u = 3^(x) and v = ln(3). Since ln(3) is a constant, its derivative is 0, and the derivative of 3^(x) is again 3^(x) * ln(3). So, (d^(2)y)/(dx^(2)) = (3^(x) * ln(3))' * ln(3) + 3^(x) * ln(3) * 0.Apply Product Rule: Simplify the expression. (d^(2)y)/(dx^(2)) = (3^(x) * ln(3) * ln(3)) + 3^(x) * ln(3) * 0. Since anything times 0 is 0, the second term disappears. (d^(2)y)/(dx^(2)) = 3^(x) * (ln(3))^2.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let
y=3^(x).
Find
(d^(2)y)/(dx^(2))

(d^(2)y)/(dx^(2))=

Let $y=3^{x}$ . $\newline$ Find $\frac{d^{2} y}{d x^{2}}$ $\newline$ $\frac{d^{2} y}{d x^{2}}=$

View step-by-step help

Home

Math Problems

Algebra 2

Simplify variable expressions using properties

Full solution

Q. Let

y=3^{x}

\newline

Find

\frac{d^{2} y}{d x^{2}}

\newline

\frac{d^{2} y}{d x^{2}}=

Find Second Derivative: Now, we need to find the second derivative $(d^{2}y)/(dx^{2})$ . We differentiate $dy/dx = 3^{x} \cdot \ln(3)$ with respect to $x$ again. Using the product rule, $(d/dx)(u\cdot v) = u'v + uv'$ , where $u = 3^{x}$ and $v = \ln(3)$ . Since $\ln(3)$ is a constant, its derivative is $0$ , and the derivative of $3^{x}$ is again $3^{x} \cdot \ln(3)$ . So, $dy/dx = 3^{x} \cdot \ln(3)$ $0$ .
Apply Product Rule: Simplify the expression. $\newline$ $\frac{d^{2}y}{dx^{2}} = 3^{x} \cdot \ln(3) \cdot \ln(3)$ + $3^{x} \cdot \ln(3) \cdot 0$ . $\newline$ Since anything times $0$ is $0$ , the second term disappears. $\newline$ $\frac{d^{2}y}{dx^{2}} = 3^{x} \cdot (\ln(3))^{2}$ .